GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 22 Aug 2019, 17:41

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Ye Olde Arte has a large supply of colored poster board. The colors ar

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
Joined: 13 Jul 2010
Posts: 1
Ye Olde Arte has a large supply of colored poster board. The colors ar  [#permalink]

Show Tags

New post 25 Mar 2011, 15:12
1
9
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

37% (01:42) correct 63% (02:33) wrong based on 19 sessions

HideShow timer Statistics

Ye Olde Arte has a large supply of colored poster board. The colors are blue, green, beige, white, yellow, and red. How many different ways can the store package 5 poster boards?

A. 126
B. 231
C. 252
D.378
E. 462
CEO
CEO
User avatar
B
Joined: 17 Nov 2007
Posts: 3307
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
GMAT ToolKit User
Re: Ye Olde Arte has a large supply of colored poster board. The colors ar  [#permalink]

Show Tags

New post 28 Mar 2011, 17:54
Good question!

Here is probably not the shortest way:

5 colors: \(C^6_5 = 6\) - 5 colors out of 6.
4 colors: \(C^6_4 * C^4_1 = 15*4 = 60\) - 4 colors out of 6 and one of 4 colors are used twice.
3 colors: \(C^6_3 * (C^3_1 + C^3_1) = 20*6 = 120\) - 3 colors out of 6 and one color of 3 for 3+1+1 combination and one color of 3 for 2+2+1 combination.
2 colors: \(C^6_2 * (C^2_1 + C^2_1) = 15*4 = 60\) - 2 colors out of 6 and one color of 2 for 3+2 combination and one color of 2 for 4+1 combination.
1 color: \(C^6_1 = 6\) - 1 color out of 6.

6+60+120+60+6 = 252
_________________
HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | Limited GMAT/GRE Math tutoring in Chicago
Retired Moderator
avatar
B
Joined: 16 Nov 2010
Posts: 1345
Location: United States (IN)
Concentration: Strategy, Technology
Reviews Badge
Re: Ye Olde Arte has a large supply of colored poster board. The colors ar  [#permalink]

Show Tags

New post 28 Mar 2011, 19:17
Hi Walker

Please explain this :

one color of 3 for 3+1+1 combination and one color of 3 for 2+2+1 combination.

Regards,
Subhash
_________________
Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings
CEO
CEO
User avatar
B
Joined: 17 Nov 2007
Posts: 3307
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
GMAT ToolKit User
Re: Ye Olde Arte has a large supply of colored poster board. The colors ar  [#permalink]

Show Tags

New post 28 Mar 2011, 20:36
If we have only 3 colors for 5 boards, there are only 2 possible options 3 (first color) + 1 (second color) + 1 (third color) and 2(first color) + 2 (second color) + 1 (third color). There is 3 different ways for each option.

For example, option 1 if we have red, green, blue:

red + green + blue + blue + blue
red + green + green + green + blue
red + red + red + green + blue

option 2:

red + red + green + green + blue
red + red + green + blue + blue
red + green + green + blue + blue

So, \(C^3_1\) actually means that we choose one color out of 3 for 3 boards (option 1) or for 1 board (option 2)
_________________
HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | Limited GMAT/GRE Math tutoring in Chicago
Retired Moderator
avatar
B
Joined: 16 Nov 2010
Posts: 1345
Location: United States (IN)
Concentration: Strategy, Technology
Reviews Badge
Re: Ye Olde Arte has a large supply of colored poster board. The colors ar  [#permalink]

Show Tags

New post 30 Mar 2011, 01:37
For 3 colors: one color of 3 for 3+1+1 combination and one color of 3 for 2+2+1 combination.

Can we write for the option 2 as 6C3 * 3C2 (which is equal to 6C3 * 3C1) ?

This is because let us say we have chosen 3 colors for 3 boards, and now we need to choose 2 colors out of 3 for the remaining 2 boards.

So option is 6C3 * 3C1 + 6C3 * 3C2.
_________________
Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings
CEO
CEO
User avatar
B
Joined: 17 Nov 2007
Posts: 3307
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
GMAT ToolKit User
Re: Ye Olde Arte has a large supply of colored poster board. The colors ar  [#permalink]

Show Tags

New post 30 Mar 2011, 04:14
Yup, \(C^3_2\) is correct too.
_________________
HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | Limited GMAT/GRE Math tutoring in Chicago
Director
Director
avatar
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 938
Re: Ye Olde Arte has a large supply of colored poster board. The colors ar  [#permalink]

Show Tags

New post 18 May 2011, 22:56
good question indeed.
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 12068
Re: Ye Olde Arte has a large supply of colored poster board. The colors ar  [#permalink]

Show Tags

New post 25 Mar 2019, 19:53
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: Ye Olde Arte has a large supply of colored poster board. The colors ar   [#permalink] 25 Mar 2019, 19:53
Display posts from previous: Sort by

Ye Olde Arte has a large supply of colored poster board. The colors ar

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne